a. Field of the Invention
The present invention relates to methods for obtaining improved two dimensional nuclear magnetic resonance (NMR) images from those disclosed in the art. The use of time varying magnetic field gradients such that the frequency history of the spins is every element of a two dimensional array is distinguishable from that of every other element in that array have been described in the art. However, the methods described in the art do not, in fact, provide tractible approaches for obtaining two dimensional NMR images from the use of such time varying magnetic field gradients.
b. Description of the Prior Art
A number of NMR techniques for spacial mapping of points, lines, and planes in a sample of matter are known in the art. The particular procedure whereby the use of time varying magnetic field gradients such that the frequency history of each element in an array is distinguishable from that of every other element in that array has been suggested in the patent to Likes (U.S. Pat. No. 4,307,343).
However, the methods described by Likes suffer from a number of shortcomings. First, Likes fails to recognize the necessity of an appropriate weighting function which is required for image reconstruction, and is necessitated by the use of gradient magnetic fields whose trajectories in phase space do not sample equal areas of that space during equal time intervals.
For example, beginning at column 10, line 27, Likes discloses the use of Lissajous, "bull's eye" and rosette trajectories as the time varying magnetic field gradients to achieve spatial differentiation. However, none of these trajectories map equal areas of space over equal time intervals. Accordingly, inaccuracies result from the use of the methods disclosed in the Likes patent to reconstruct the image, without compensating for the nonlinear relationship of the trajectory's path in phase space with respect to time.
It is therefore an object of the present invention to provide novel methods for NMR mapping of two dimensional samples of matter whereby magnetic field gradients map equal areas of phase space in equal intervals of time.
It is yet another object of the present invention to provide methods for NMR mapping whereby magnetic field gradients may equal areas of phase space in unequal intervals of time, which times can be obtained from an appropriate weighing function.
It is yet a further object of this invention to provide novel reconstruction methods for reconstructing two dimensional images from NMR information obtained from samples of matter while utilizing gradient magnetic fields having trajectories that do not sample equal areas of phase space during equal intervals of time.